Question

graph $y = \frac{4}{5}x - 7$.

Explanation:

Step1: Identify the slope-intercept form

The equation \( y = \frac{4}{5}x - 7 \) is in slope - intercept form \( y=mx + b \), where \( m=\frac{4}{5} \) (slope) and \( b=-7 \) (y - intercept).

Step2: Find the y - intercept

The y - intercept \( b=-7 \), so the line crosses the y - axis at the point \( (0,-7) \).

Step3: Use the slope to find another point

The slope \( m = \frac{4}{5}\) means "rise over run", or \( \frac{\text{change in }y}{\text{change in }x}\). From the y - intercept \( (0,-7) \), we can rise 4 units (since the numerator of the slope is 4) and run 5 units to the right (since the denominator of the slope is 5). So from \( (0,-7) \), adding 4 to the y - coordinate and 5 to the x - coordinate, we get the point \( (0 + 5,-7+4)=(5,-3) \).

Step4: Plot the points and draw the line

Plot the points \( (0,-7) \) and \( (5,-3) \) on the coordinate plane. Then draw a straight line passing through these two points. The given graph in the problem is incorrect as it shows a horizontal line (which would have a slope of 0, but our equation has a slope of \( \frac{4}{5}\)). The correct graph should be a line with a positive slope, passing through \( (0,-7) \) and \( (5,-3) \) (and other points found using the slope).

Answer:

To graph \( y=\frac{4}{5}x - 7 \):

1. Plot the y - intercept at \( (0,-7) \).
2. Use the slope \( \frac{4}{5} \) to find another point: from \( (0,-7) \), move 5 units right and 4 units up to get \( (5,-3) \).
3. Draw a straight line through \( (0,-7) \) and \( (5,-3) \). The given graph is incorrect; the correct graph has a positive slope, passing through \( (0,-7) \) and \( (5,-3) \).